The liquid-phase dimerization of C5H6, 2 C5H6 ? C10H12, is studied at a certain
ID: 733939 • Letter: T
Question
The liquid-phase dimerization of C5H6, 2 C5H6 ? C10H12, is studied at a certain temperature, givingthe following data:
Time (s): 0.0e+00 1.0e+02 2.0e+02 3.0e+02 4.0e+02
[C5H6] (M): 0.100 0.0265 0.0153 0.0107 0.00828
??Figure out whether this reaction is first-order or second-order with respect to the concentration of C5H6.
Then Calculate the value of the rate constant.
Pick the choice from below which gives the correct reaction order and value of the rate constant for this reaction.
a) This reaction is first-order with the rate constant k = 6.93e-02 s-1.
b) This reaction is second-order with the rate constant k = 8.31e-01 M-1 s-1.
c) This reaction is second-order with the rate constant k = 2.77e-01 M-1 s-1.
d) This reaction is second-order with the rate constant k = 1.66e+00 M-1 s-1.
e) This reaction is first-order with the rate constant k = 5.54e-01 s-1.
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Explanation / Answer
c) This reaction is second-order with the rate constant k = 2.77e-01 M-1 s-1. A first order reaction will have the relation: ln[A] = -kt + ln[A0], where [A] is the concentration at some time t, and [A0] is the concentration at t = 0. A second order reaction will have the relation: 1/[A] = 1/[A0] + kt These relations suggest that the reaction is 1st order when there a linear relationship of log transformed [C5H6] values over time, and second order when there is a linear relationship of inverse [C6H6] values over time. Given the data, we can transform the data using the natural log or inverse of each concentration value of [C5H6]. Then we plot the transformed [C5H6] as a function of time and see which order gives a linear plot. It turns out that the inverse of [C5H6] gives this linear plot. Therefore the reaction is second order with respect to [C5H6]. To find the value of k, we simply plug in any two values to the inverse relation. Let's do [C5H6] at t = 200 sec 1/0.0153 = 1/0.1 + k*200 ==> k = 0.277 M-1 s-1 or choice C
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